jee-main

Papers (191)
2026
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2025
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2024
session1_01feb_shift1 5 session1_01feb_shift2 21 session1_27jan_shift1 28 session1_27jan_shift2 30 session1_29jan_shift1 28 session1_29jan_shift2 29 session1_30jan_shift1 20 session1_30jan_shift2 29 session1_31jan_shift1 16 session1_31jan_shift2 15 session2_04apr_shift1 5 session2_04apr_shift2 28 session2_05apr_shift1 4 session2_05apr_shift2 30 session2_06apr_shift1 21 session2_06apr_shift2 30 session2_08apr_shift1 30 session2_08apr_shift2 29 session2_09apr_shift1 8 session2_09apr_shift2 30
2023
session1_01feb_shift1 28 session1_01feb_shift2 3 session1_24jan_shift1 11 session1_24jan_shift2 11 session1_25jan_shift1 29 session1_25jan_shift2 29 session1_29jan_shift1 29 session1_29jan_shift2 28 session1_30jan_shift1 5 session1_30jan_shift2 27 session1_31jan_shift1 28 session1_31jan_shift2 15 session2_06apr_shift1 5 session2_06apr_shift2 16 session2_08apr_shift1 29 session2_08apr_shift2 13 session2_10apr_shift1 29 session2_10apr_shift2 16 session2_11apr_shift1 6 session2_11apr_shift2 8 session2_12apr_shift1 26 session2_13apr_shift1 24 session2_13apr_shift2 24 session2_15apr_shift1 19
2022
session1_24jun_shift1 19 session1_24jun_shift2 25 session1_25jun_shift1 14 session1_25jun_shift2 14 session1_26jun_shift1 29 session1_26jun_shift2 24 session1_27jun_shift1 4 session1_27jun_shift2 29 session1_28jun_shift1 13 session1_29jun_shift1 20 session1_29jun_shift2 4 session2_25jul_shift1 29 session2_25jul_shift2 20 session2_26jul_shift1 29 session2_26jul_shift2 23 session2_27jul_shift1 28 session2_27jul_shift2 29 session2_28jul_shift1 11 session2_28jul_shift2 29 session2_29jul_shift1 17 session2_29jul_shift2 18
2021
session1_24feb_shift1 9 session1_24feb_shift2 4 session1_25feb_shift1 29 session1_25feb_shift2 29 session1_26feb_shift2 15 session2_16mar_shift1 29 session2_16mar_shift2 18 session2_17mar_shift1 21 session2_17mar_shift2 27 session2_18mar_shift1 18 session2_18mar_shift2 9 session3_20jul_shift1 29 session3_20jul_shift2 29 session3_22jul_shift1 9 session3_25jul_shift1 8 session3_25jul_shift2 14 session3_27jul_shift1 4 session3_27jul_shift2 7 session4_01sep_shift2 14 session4_26aug_shift1 5 session4_26aug_shift2 2 session4_27aug_shift1 3 session4_27aug_shift2 29 session4_31aug_shift1 28 session4_31aug_shift2 4
2020
session1_07jan_shift1 28 session1_07jan_shift2 20 session1_08jan_shift1 5 session1_08jan_shift2 11 session1_09jan_shift1 26 session1_09jan_shift2 16 session2_02sep_shift1 18 session2_02sep_shift2 16 session2_03sep_shift1 23 session2_03sep_shift2 8 session2_04sep_shift1 14 session2_04sep_shift2 27 session2_05sep_shift1 22 session2_05sep_shift2 29 session2_06sep_shift1 11 session2_06sep_shift2 10
2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 29 session1_10jan_shift2 14 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 29 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 5 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 30 15apr 28 15apr_shift1 28 15apr_shift2 6 16apr 19
2017
02apr 30 08apr 30 09apr 34
2016
03apr 28 09apr 29 10apr 30
2015
04apr 29 10apr 29 11apr 8
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 12 22apr 5 23apr 14 25apr 13
2012
07may 17 12may 21 19may 14 26may 17 offline 30
2011
jee-main_2011.pdf 18
2010
jee-main_2010.pdf 6
2009
jee-main_2009.pdf 2
2008
jee-main_2008.pdf 4
2007
jee-main_2007.pdf 38
2006
jee-main_2006.pdf 15
2005
jee-main_2005.pdf 25
2004
jee-main_2004.pdf 22
2003
jee-main_2003.pdf 8
2002
jee-main_2002.pdf 12
2024 session1_29jan_shift2

29 maths questions

Q4 Work done and energy Energy conservation with friction or dissipative forces View
The bob of a pendulum was released from a horizontal position. The length of the pendulum is 10 m. If it dissipates $10 \%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is: [Use, $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
(1) $6 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $5 \sqrt { 6 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $5 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $2 \sqrt { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$
Q5 Circular Motion 1 Conservation of energy on frictionless tracks and pendulums View
A bob of mass $m$ is suspended by a light string of length $L$. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$. The ratio of kinetic energies $\frac { ( \text { K.E. } ) _ { A } } { ( \text { K.E. } ) _ { B } }$ is:
(1) $3 : 2$
(2) $5 : 1$
(3) $2 : 5$
(4) $1 : 5$
Q6 Circular Motion 1 Centripetal Acceleration / Force Calculation View
A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?
(1) 25
(2) 50
(3) 100
(4) 20
Q7 Advanced work-energy problems View
A wire of length $L$ and radius $r$ is clamped at one end. If its other end is pulled by a force $F$, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:
(1) 3 times
(2) $\frac { 3 } { 2 }$ times
(3) 4 times
(4) 2 times
Q8 Advanced work-energy problems View
A small liquid drop of radius $R$ is divided into 27 identical liquid drops. If the surface tension is $T$, then the work done in the process will be:
(1) $8 \pi R ^ { 2 } T$
(2) $3 \pi R ^ { 2 } T$
(3) $\frac { 1 } { 8 } \pi R ^ { 2 } T$
(4) $4 \pi R ^ { 2 } T$
Q21 Circular Motion 1 Non-Uniform Circular Motion (Tangential + Centripetal) View
A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at $\mathrm { t } = 0$ is $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the time taken to complete the first revolution will be $\frac { 1 } { \alpha } \left[ 1 - \mathrm { e } ^ { - 2 \pi } \right] \mathrm { s }$, where $\alpha =$ $\_\_\_\_$ .
Q22 Momentum and Collisions Assertion-Reason or Statement-Based Conceptual View
A body of mass 5 kg moving with a uniform speed $3 \sqrt { 2 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in $X - Y$ plane along the line $y = x + 4$. The angular momentum of the particle about the origin will be $\_\_\_\_$ $\mathrm { kg } \mathrm { m } ^ { 2 } \mathrm {~s} ^ { - 1 }$.
Q23 Advanced work-energy problems View
Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4 : 1$ and force $F _ { 1 }$ is applied to $P$, an extension of $\Delta l$ is produced. The force which is required to produce same extension in Q is $F _ { 2 }$. The value of $\frac { F _ { 1 } } { F _ { 2 } }$ is $\_\_\_\_$ .
Q24 Simple Harmonic Motion View
A simple harmonic oscillator has an amplitude $A$ and time period $6 \pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $x = A$ to $x = \frac { \sqrt { 3 } } { 2 } A$ will be $\frac { \pi } { x } \mathrm {~s}$, where $x =$ $\_\_\_\_$ .
Q61 Complex Numbers Arithmetic Locus Identification from Modulus/Argument Equation View
Let $r$ and $\theta$ respectively be the modulus and amplitude of the complex number $z = 2 - i \left( 2 \tan \frac { 5 \pi } { 8 } \right)$, then $( r , \theta )$ is equal to
(1) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$
(2) $\left( 2 \sec \frac { 3 \pi } { 8 } , \frac { 5 \pi } { 8 } \right)$
(3) $\left( 2 \sec \frac { 5 \pi } { 8 } , \frac { 3 \pi } { 8 } \right)$
(4) $\left( 2 \sec \frac { 11 \pi } { 8 } , \frac { 11 \pi } { 8 } \right)$
Q62 Permutations & Arrangements Distribution of Objects into Bins/Groups View
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
(1) 18
(2) 16
(3) 12
(4) 15
Q63 Arithmetic Sequences and Series Properties of AP Terms under Transformation View
If $\log _ { e } a , \log _ { e } b , \log _ { e } c$ are in an $A . P$. and $\log _ { e } a - \log _ { e } 2 b , \log _ { e } 2 b - \log _ { e } 3 c , \log _ { e } 3 c - \log _ { e } a$ are also in an $A . P$. , then $a : b : c$ is equal to
(1) $9 : 6 : 4$
(2) $16 : 4 : 1$
(3) $25 : 10 : 4$
(4) $6 : 3 : 2$
Q64 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
If each term of a geometric progression $\mathrm { a } _ { 1 } , \mathrm { a } _ { 2 } , \mathrm { a } _ { 3 } , \ldots$ with $\mathrm { a } _ { 1 } = \frac { 1 } { 8 }$ and $\mathrm { a } _ { 2 } \neq \mathrm { a } _ { 1 }$, is the arithmetic mean of the next two terms and $\mathrm { S } _ { \mathrm { n } } = \mathrm { a } _ { 1 } + \mathrm { a } _ { 2 } + \ldots + \mathrm { a } _ { \mathrm { n } }$, then $\mathrm { S } _ { 20 } - \mathrm { S } _ { 18 }$ is equal to
(1) $2 ^ { 15 }$
(2) $- 2 ^ { 18 }$
(3) $2 ^ { 18 }$
(4) $- 2 ^ { 15 }$
Q65 Standard trigonometric equations Trigonometric equation with algebraic or logarithmic coupling View
The sum of the solutions $x \in R$ of the equation $\frac { 3 \cos 2 x + \cos ^ { 3 } 2 x } { \cos ^ { 6 } x - \sin ^ { 6 } x } = x ^ { 3 } - x ^ { 2 } + 6$ is
(1) 0
(2) 1
(3) - 1
(4) 3
Q66 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
Let $A$ be the point of intersection of the lines $3 x + 2 y = 14,5 x - y = 6$ and $B$ be the point of intersection of the lines $4 x + 3 y = 8,6 x + y = 5$. The distance of the point $P ( 5 , - 2 )$ from the line $A B$ is
(1) $\frac { 13 } { 2 }$
(2) 8
(3) $\frac { 5 } { 2 }$
(4) 6
Q67 Straight Lines & Coordinate Geometry Point-to-Line Distance Computation View
The distance of the point $( 2,3 )$ from the line $2 x - 3 y + 28 = 0$, measured parallel to the line $\sqrt { 3 } x - y + 1 = 0$, is equal to
(1) $4 \sqrt { 2 }$
(2) $6 \sqrt { 3 }$
(3) $3 + 4 \sqrt { 2 }$
(4) $4 + 6 \sqrt { 3 }$
Q68 Measures of Location and Spread View
If the mean and variance of five observations are $\frac { 24 } { 5 }$ and $\frac { 194 } { 25 }$ respectively and the mean of first four observations is $\frac { 7 } { 2 }$, then the variance of the first four observations is equal to
(1) $\frac { 4 } { 5 }$
(2) $\frac { 77 } { 12 }$
(3) $\frac { 5 } { 4 }$
(4) $\frac { 105 } { 4 }$
Q69 Probability Definitions Computation of a Limit, Value, or Explicit Formula View
If $R$ is the smallest equivalence relation on the set $\{ 1,2,3,4 \}$ such that $\{ ( 1,2 ) , ( 1,3 ) \} \subset R$, then the number of elements in $R$ is
(1) 10
(2) 12
(3) 8
(4) 15
Q70 3x3 Matrices Determinant of Parametric or Structured Matrix View
Let $\mathrm { A } = \left[ \begin{array} { c c c } 2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2 \end{array} \right]$ and $\mathrm { P } = \left[ \begin{array} { l l l } 1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5 \end{array} \right]$. The sum of the prime factors of $\left| \mathrm { P } ^ { - 1 } \mathrm { AP } - 2 \mathrm { I } \right|$ is equal to
(1) 26
(2) 27
(3) 66
(4) 23
Q71 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
Let $x = \frac { m } { n } \left( m , n \right.$ are co-prime natural numbers) be a solution of the equation $\cos \left( 2 \sin ^ { - 1 } x \right) = \frac { 1 } { 9 }$ and let $\alpha , \beta ( \alpha > \beta )$ be the roots of the equation $m x ^ { 2 } - n x - m + n = 0$. Then the point $( \alpha , \beta )$ lies on the line
(1) $3 x + 2 y = 2$
(2) $5 x - 8 y = - 9$
(3) $3 x - 2 y = - 2$
(4) $5 x + 8 y = 9$
Q72 Chain Rule Higher-order or nth derivative computation View
Let $y = \log _ { e } \left( \frac { 1 - x ^ { 2 } } { 1 + x ^ { 2 } } \right) , - 1 < x < 1$. Then at $x = \frac { 1 } { 2 }$, the value of $225 \left( y ^ { \prime } - y ^ { \prime \prime } \right)$ is equal to
(1) 732
(2) 746
(3) 742
(4) 736
Q73 Stationary points and optimisation Find critical points and classify extrema of a given function View
The function $f ( x ) = 2 x + 3 x ^ { \frac { 2 } { 3 } } , x \in R$, has
(1) exactly one point of local minima and no point of local maxima
(2) exactly one point of local maxima and no point of local minima
(3) exactly one point of local maxima and exactly one point of local minima
(4) exactly two points of local maxima and exactly one point of local minima
Q74 Stationary points and optimisation Determine intervals of increase/decrease or monotonicity conditions View
The function $f ( x ) = \frac { x } { x ^ { 2 } - 6 x - 16 } , x \in \mathbb { R } - \{ - 2,8 \}$
(1) decreases in $( - 2,8 )$ and increases in $( - \infty , - 2 ) \cup ( 8 , \infty )$
(2) decreases in $( - \infty , - 2 ) \cup ( - 2,8 ) \cup ( 8 , \infty )$
(3) decreases in $( - \infty , - 2 )$ and increases in $( 8 , \infty )$
(4) increases in $( - \infty , - 2 ) \cup ( - 2,8 ) \cup ( 8 , \infty )$
Q75 Integration by Substitution Substitution to Compute an Indefinite Integral with Initial Condition View
If $\int \frac { \sin ^ { \frac { 3 } { 2 } } x + \cos ^ { \frac { 3 } { 2 } } x } { \sqrt { \sin ^ { 3 } x \cos ^ { 3 } x \sin ( x - \theta ) } } d x = A \sqrt { \cos \theta \tan x - \sin \theta } + B \sqrt { \cos \theta - \sin \theta \cot x } + C$, where $C$ is the integration constant, then $AB$ is equal to
(1) $4 \operatorname { cosec } ( 2 \theta )$
(2) $4 \sec \theta$
(3) $2 \sec \theta$
(4) $8 \operatorname { cosec } ( 2 \theta )$
Q76 First order differential equations (integrating factor) Solving Separable DEs with Initial Conditions View
If $\sin \left( \frac { y } { x } \right) = \log _ { e } | x | + \frac { \alpha } { 2 }$ is the solution of the differential equation $x \cos \left( \frac { y } { x } \right) \frac { d y } { d x } = y \cos \left( \frac { y } { x } \right) + x$ and $y ( 1 ) = \frac { \pi } { 3 }$, then $\alpha ^ { 2 }$ is equal to
(1) 3
(2) 12
(3) 4
(4) 9
Q77 Vectors Introduction & 2D Area Computation Using Vectors View
Let $\overrightarrow { \mathrm { OA } } = \overrightarrow { \mathrm { a } } , \overrightarrow { \mathrm { OB } } = 12 \overrightarrow { \mathrm { a } } + 4 \overrightarrow { \mathrm {~b} }$ and $\overrightarrow { \mathrm { OC } } = \overrightarrow { \mathrm { b } }$, where O is the origin. If $S$ is the parallelogram with adjacent sides OA and OC, then $\frac { \text { area of the quadrilateral } \mathrm { OABC } } { \text { area of } \mathrm { S } }$ is equal to
(1) 6
(2) 10
(3) 7
(4) 8
Q78 Vectors Introduction & 2D Vector Algebra and Triple Product Computation View
Let a unit vector $\widehat { u } = x \hat { i } + y \hat { j } + z \widehat { k }$ make angles $\frac { \pi } { 2 } , \frac { \pi } { 3 }$ and $\frac { 2 \pi } { 3 }$ with the vectors $\frac { 1 } { \sqrt { 2 } } \hat { i } + \frac { 1 } { \sqrt { 2 } } \widehat { k } , \frac { 1 } { \sqrt { 2 } } \hat { j } + \frac { 1 } { \sqrt { 2 } } \widehat { k }$ and $\frac { 1 } { \sqrt { 2 } } \hat { i } + \frac { 1 } { \sqrt { 2 } } \hat { j }$ respectively. If $\vec { v } = \frac { 1 } { \sqrt { 2 } } \hat { i } + \frac { 1 } { \sqrt { 2 } } \hat { j } + \frac { 1 } { \sqrt { 2 } } \hat { k }$, then $| \hat { u } - \vec { v } | ^ { 2 }$ is equal to
(1) $\frac { 11 } { 2 }$
(2) $\frac { 5 } { 2 }$
(3) 9
(4) 7
Q79 Vectors 3D & Lines Vector Algebra and Triple Product Computation View
Let $\mathrm { P } ( 3,2,3 ) , \mathrm { Q } ( 4,6,2 )$ and $\mathrm { R } ( 7,3,2 )$ be the vertices of $\triangle \mathrm { PQR }$. Then, the angle $\angle \mathrm { QPR }$ is
(1) $\frac { \pi } { 6 }$
(2) $\cos ^ { - 1 } \left( \frac { 7 } { 18 } \right)$
(3) $\cos ^ { - 1 } \left( \frac { 1 } { 18 } \right)$
(4) $\frac { \pi } { 3 }$
Q80 Principle of Inclusion/Exclusion View
An integer is chosen at random from the integers $1,2,3 , \ldots , 50$. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is
(1) $\frac { 8 } { 25 }$
(2) $\frac { 21 } { 50 }$